18 citations · 64 across the 8 of their papers we have counts for
5 papers · 1 filter
Some observations on high-dimensional partial differential equations with Barron data
Weinan E, Stephan Wojtowytsch
We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such funct…
On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime
Stephan Wojtowytsch
We describe a necessary and sufficient condition for the convergence to minimum Bayes risk when training two-layer ReLU-networks by gradient descent in the mean field regime with o…
On the motion of curved dislocations in three dimensions: Simplified linearized elasticity
Irene Fonseca, Janusz Ginster, Stephan Wojtowytsch
It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetriz…
Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields
Patrick Dondl, Matteo Novaga, Benedikt Wirth +1
We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional…
On the Boundary Regularity of Phase-Fields for Willmore's Energy
Patrick Dondl, Stephan Wojtowytsch
We demonstrate that Radon measures which arise as the limit of the Modica-Mortola measures associated to phase-fields with uniformly bounded diffuse area and Willmore energy may be…